Math Problem Statement

The square on the right is a scaled copy of the square on the left. Identify the scale factor. Express your answer as a fraction in simplest form. 5 5 12 12

Solution

To determine the scale factor between the two squares, we need to compare the side lengths of the smaller square to the corresponding side lengths of the larger square.

  • The side length of the smaller square is given as 5 units.
  • The side length of the larger square is given as 12 units.

The scale factor is the ratio of the side length of the smaller square to the side length of the larger square:

Scale factor=Side length of smaller squareSide length of larger square=512\text{Scale factor} = \frac{\text{Side length of smaller square}}{\text{Side length of larger square}} = \frac{5}{12}

Thus, the scale factor is 512\frac{5}{12}.

Would you like more details or have any questions? Here are some related questions to explore:

  1. How do you calculate the area of the smaller square using the side length?
  2. What is the area of the larger square?
  3. How does the scale factor affect the area of the squares?
  4. If the side length of the larger square were doubled, what would the new scale factor be?
  5. How would you find the perimeter of each square?

Tip: When finding the scale factor between similar shapes, always compare corresponding sides or dimensions.

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Math Problem Analysis

Mathematical Concepts

Geometry
Ratios
Scale Factors

Formulas

Scale factor = side length of smaller square / side length of larger square

Theorems

Similarity of figures
Proportionality in geometric shapes

Suitable Grade Level

Grades 6-8